Download Exponent, Squared, Cubed

Name:_______________________________________
Block:________ Date:___________ (SOL: 6.5)
-Word Bank for ExponentsExponent, Squared, Cubed, Exponential Form, Inverse Operations, Product Form/Standard Form, Base
4
3
5
2
4
4
3x3x3x3
34
Or
Or
Multiplication is the opposite of Division
3 3 3
33
Addition is the opposite of Subtraction
Factors
Numbers
Words
Exponential Form
4
4x4
Four to the second power
or four squared
42
2
222
Two to the third power or
23
Two CUBED
5
55
Five SQUARED
3
3333
Three to the fourth power
Any number
to the zero power is ALWAYS 1 (except 0)
Square numbers, perfect squares and square roots
To find the square root of a number, find the number that when multiplied by itself is equal
to the number. *The root MAKES the larger number or the perfect square.
Square Roots
√
square root symbol
√
= 2 because…
2 is the length of each side.
Example: √ = 4 because 4 x 4 = 16 or 42 is a square with 4 on each side
On a square all sides are the same length and one side x the other = a perfect square.
PERFECT SQUARES- Tell the square root for each perfect square.
36 = 6
81 =
25 =
Because…
Because 6 x 6 = 36
(The square root of 36 is 6.)
Because…
36 =
49 =
144 =
Because…
Because…
Because…
121 =
400 =
1=
Because…
Because…
Because…
Think about it… are the following perfect squares?
#’s
Yes
No
25
Proof: Multiplication fact
5 x 5 = 25 All sides equal/square
12
48
49
0
2
100
56
1
What if it is NOT a perfect square?
The square root of a number that is not a perfect square falls between two consecutive
whole numbers.
Step 1: Is the number 29 a perfect square? Is there a whole number which can be squared
to equal 29?______________
Step 2: A) The number 25 is the closest perfect square less than 29. What is
_______________
B) The number 36 is closest perfect square greater than 29. What is
C)
29
lies between
between which
29
25
and
25 ? -
36 ? _______________
36 . What are the two consecutive whole numbers
lies? _______________________
Perfect Square
#’s:
Square Roots:
√
TRUE or FALSE? Show your work!
A) True or False
32 = 2 3
²=
2² =
3² =
4² =
5² =
TRUE or FALSE? Show your work!
²=
7² =
B) True or False
42= 24
8² =
9² =
0² =
²=
2² =
3² =
4² =
5² =
²=
7² =
8² =
9² =
20² =
Shade all PERFECT SQUARES
Finding the square root for NON-Perfect Squares.
* Find the two consecutive WHOLE NUMBERS between which the square root
of a given number lies/falls between.
1)
19 ________
__________
2) 57 ________ __________
3)
48 ________
__________
4)
99 ________
__________
__________
5) 17
________
__________
6)
2 ________
7)
________
__________
8)
82
22
9) 133
5
1) 2
________
=2x2x2x2x2
__________
10)
________
__________
320 ________
_________
4
3) 1
4
6) 7
3
9) 8
2) 3
8
Answer: 32
1
4) 9
5) 5
8
8) 4
7) 0
2
0
A) Write the following powers as a product of the same factor (product form, x x x )
1.) 45 =
2.) 36 =
3.) 83 =
B) Evaluate, or find the value of the given problems.
4.) 63 =
5.) 24 =
6.) 43 =
C) Write the following numbers in exponential form (exponent form).
7.) Write 6  6  6  6  6  6  6 in exponential form.
8.) Write 8  8  8  8  8  8  8  8  8  8  8 in exponential form.
9.) Write 2  2  2  2  2  3  3  3  3 in exponential form.
What is the square root of each PERFECT square?
1)
√
=4
2)
√25 =
3)
√8 =
4)
√ 00 =
5)
√9 =
6)
√3 =
7)
√ 44 =
8)
√ =
9)
√49 =
10)
√4 =
11)
√ 4=
12)
√ 2 =
Write each expression in exponential form.
1)
4 x 4 x 4 x 4 x 4 x 4 _________________
2)
8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 _____________
3)
9 x 9 __________________
4)
p x p x p x p x p _______________
5)
(10)(10)(10) _________________
6)
(14s)(14s)(14s) _______________
Find the square of each number. 4 squared = 4 x 4 = 42
1)
7
2)
5) 4
13
3)
6) 10
11
4)
7) 6
1
8) 8
Circle the numbers that are PERFECT squares:
6
18
36
49
55
64
73
100
122
169
Find the square root for each of the perfect squares
1)
√ 44 =
2) √25 =
3) √8 =
4)
√ 9 =
5) √ 25 =
6) √25 =
Estimate to find the two consecutive whole numbers between which the square root of a
given number lies.
1) √ 2 ______ ______
2) √9
0 _____ ______
______ ______
3) √
4) √3 ______ ______ 5) √ 70 _____ ______6) √55 ______ ______
7) √ 50 _____ ______8) √75 ______ ______9) √44 ______ ______
Compare the following values using <, >, or =.
1)
32
3) √ 4
√ 4
2)
103
√8
4)
1
8
√4
1
5